Typical imaging systems employ the principles for a single pinhole-style camera. Referring to FIG. 1A, a schematic diagram illustrating the geometry of a conventional pinhole camera is shown. Such a conventional pinhole camera is configured for imaging of an object O emitting or reflecting radiation. In other words, the object O is the source of the emitting or reflecting radiation. The radiation is collected through the pinhole in the aperture mask A, and an image is formed at an image plane P. The image plane P is located on the opposite side of the object O relative to the aperture mask A. The direction of the radiation is represented by the direction labeled z, or the z-axis. The image formed at the image plane P does not provide any depth resolution along the z-axis because the information recorded at the image plane P is formed through a single imaging pinhole and contains all surface and internal structure of the object projected onto a 2-dimensional image plane, P.
Referring to FIG. 1B, a schematic diagram illustrates the geometry of a conventional camera employing an aperture, A, containing multiple pinholes. This camera is also configured for imaging of an object emitting or reflecting radiation, but is different from the single pinhole-style camera of FIG. 1A in that this camera employs a multi-pinhole coded aperture system instead of a single pinhole aperture.
A coded aperture system exhibits the resolution of a pinhole-style camera but with collection efficiency proportional to the number of pinholes in the aperture. The aperture is a collection of pinholes in a specified pattern. Coded aperture imaging systems represent a class of cameras that are heavily investigated today for applications ranging from national security to biomedical imaging.
For these applications, the system is designed to capture the radiation emitted from the object O. The object O could be a radioactive dispersive device, an astronomical gamma star, or an organ containing a medical isotope. The image formed at the detector plane and the reconstructed image is described according to the following relationships:P(r)=O(r)*A(r) image formation  (1)Ô(r)=P(r)*G(r) image reconstruction  (2)Ô(r)=O(r)*(A(r)*G(r)) substitution of Eq. (1) into Eq. (2)  (3)Ô(r)≈O(r) iff A(r)*G(r)≈δ(r) aperture condition  (4)where “*” is the convolution operator and r=(x,y) is a two-dimensional spatial coordinate in the object, aperture, and imaging planes. The convolution operator is defined by (ƒ*g)(x)=∫ƒ(α)g(x−α)dα. For the purposes of description of the system in FIG. 1B, an article by Fenimore, E. E. and T. M. Cannon, titled “Coded Aperture Imaging with Uniformly Redundant Arrays,” Applied Optics 17(3): 337 (1978) is incorporated herein by reference. The aperture in FIG. 1B exhibits the property that A(r)*G(r)≈δ(r), where δ(r) is the Dirac delta function. Note that the decoding aperture, G(r), is defined based on the pattern of A(r) to achieve balanced decoding as follows,
                              G          ⁡                      (            r            )                          ≡                  {                                                    1                                                                                  if                    ⁢                                                                                  ⁢                                          A                      ⁡                                              (                        r                        )                                                                              =                  1                                                                                                      -                  1                                                                                                  if                    ⁢                                                                                  ⁢                                          A                      ⁡                                              (                        r                        )                                                                              =                  0                                                                                        (        5        )            
Many imaging devices employ a different geometry than the geometry shown in FIGS. 1A and 1B. An object emitting radiation imaged with a single pinhole provides radiation that passes through the hole and impinges on the detector plane. The radiation is detected by a radiation sensor in the detector plane to generate an image of the object.
Imaging efficiency is a concern for many imaging devices employing a radiation source because the radiation source typically generates a radiation of limited intensity. Where generation of radiation of sufficient intensity is a challenge, imaging devices employing such radiation tend to suffer from poor spatial resolution. Such radiation sources include X-ray sources, neutron sources, gamma ray sources, proton sources, etc.
Many radiation sources with limited intensity fall in the category of non-diffracting radiation sources or refracting radiation sources. Non-diffracting radiation sources refer to radiation sources that provide a radiation that does not substantially diffract. Diffraction is an inherent property of all waves that interact at the interface of differing materials, or a vacuum and material interface. Electromagnetic radiation has a wavelength given by c/f, in which c is the speed of light in the medium and f is the frequency of the radiation. Radiations of a material wave has a wavelength given by h/p, in which h is Plank's constant and p is the momentum of the radiated particle. The wavelength of the material wave is also called the de Broglie wavelength.
The diffractive property of a wave is manifested when the dimensions of geometric features in the path of a radiation is comparable with the wavelength of the radiation. Thus, even though all radiations are diffracting in the strictest sense, the diffractive properties are displayed only when the dimensions of geometric features are on the order of, or less than, the wavelength of the radiation. Otherwise, the diffractive properties of the radiation is insignificant and unobservable, and the radiation does not “substantially diffract,” i.e., the radiation is considered a non-diffracting radiation. For example, X-ray, neutrons, gamma ray, and protons are employed in imaging devices in which the aperture is much greater than the wavelength of the radiation.
Refraction is another inherent property of radiation. Refraction is the change in direction of a wave due to a change in the phase velocity across different mediums. When a radiation is refracted by an object, the presence of the object can be indirectly detected by a change in the image.
Since imaging efficiency has a direct impact on resolution of images, difficulty in obtaining high radiation intensity from various non-diffracting or refracting radiation sources limits resolution of images obtained using such radiation sources. Particularly, biomedical imaging devices employing such a radiation source of insufficient intensity generate a low resolution image of a patient. For example, the best neutron radiography systems throughout the world today achieve spatial resolutions no better than 100 microns because it is not possible to focus, i.e., through diffraction and refraction, a beam of neutrons to achieve a high efficiency of collection. Neutron radiography has long been known to provide complementary, non-destructive capabilities to x-ray and gamma-ray imaging methods. Neutron imaging with conventional reactor-based sources enables the interrogation of complex, multi-component systems for many applications including nuclear material non-destructive testing, characterization of flight control surfaces on aircraft, testing of heat transfer in porous materials, heat exchanger systems, and biological systems. Newer, intense neutron sources from spallation facilities are providing the potential to interrogate time and energy-dependent phenomena as well.
Thus, spatial resolution achieved by conventional neutron radiography is limited today by the sample rate at the detector and by the limited intensity of neutron beams. Because neutron beams are marginally-diffracting or refracting at microscopic and macroscopic scales, neutron optics that can magnify or de-magnify (i.e., focus) imaged objects are difficult to create and require expensive designs and materials.
Such a limitation on resolution adversely affects performance of imaging devices. Therefore, there is a need for an imaging device that provides enhanced resolution despite limited radiation intensity from a non-diffracting or refracting radiation source. Further, there is a need for a method for operating such imaging devices and a program designed to perform the operation of such imaging devices.